Wee was born into a Hoklo family with ancestry from Quemoy island on 22 July 1890 in Kuching, Sarawak, a British protectorate (now part of Malaysia).
His father was Wee Tee Yah (died 1889), and his mother was Song Kim Keow, a local born widow.
The younger Wee attended Saint Thomas Secondary School and spoke both Hokkien as well as English fluently.
[8] The Kapitan Cina Ong Tiang Swee (Chinese: 王長水; pinyin: Wáng Chángshuǐ), who was then Kuching's wealthiest person, was impressed by Wee, and decided to let him marry his eldest daughter, Ong Siew Eng (Chinese: 王秀英; pinyin: Wáng Xiùyīng).
His fourth son, Wee Cho Yaw, was subsequently appointed to head United Overseas Bank.